Variational and numerical analysis of a frictionless contact problem for elastic-viscoplastic materials with internal state variables

We consider a quasistatic frictionless contact problem between a deformable body and a foundation. The material is assumed to have a nonlinear behavio ur that we model with a rate-type viscoplastic constitutive law involving i nternal state variables. The contact is modelled with normal compliance. We present a variational formulation of the problem and prove the existence a nd uniqueness of the weak solution. We then derive error estimates for a fu lly discrete scheme to solve the problem. Under appropriate regularity assu mptions on the exact solution, we establish optimal-order error estimates. Finally, we present numerical examples which show a very good performance o f the fully discrete scheme.